Aimed at the problem that the particle swarm optimization (PSO) algorithm has a poor global search capability and is easy to fall into local optimum when it is applied to the selective harmonic elimination pulse width modulation (SHEPWM) of an inverter, an improved PSO algorithm is proposed. The vertical crossover operation of genetic algorithm is introduced to the search process, and the elite retention strategy is used to improve the global and local search capabilities of the algorithm and retain excellent individuals, thereby increasing the accuracy of switching angle and improving the performance of SHEPWM. This algorithm is used to solve the SHEPWM nonlinear transcendental equation of a novel asymmetric cascaded switched capacitor multi-level inverter, which overcomes problems such as the high dependence of traditional numerical methods on initial value and the low accuracy of the traditional PSO algorithm in solving the switching angle. Finally, the feasibility of the proposed topology and the effectiveness of the proposed algorithm applied to SHEPWM were verified by simulation and experimental results.